Nobody is quite sure. Sometime after the development of the nucleus and membrane bound organelles is about the best we can say. IOW the common ancestor of animals and plants was already a eukaryote. Beyond that it gets very hard to give a definitive answer.
One of the main reasons it’s so hard to give a definitive answer is because it’s very difficult to give a definitive definition of animals and plants. Sponges for example are commonly called animals, but they are far more closely related to protists than they are to the other animals. Similarly some types of algae are considered plants while their closest relative are considered to be algal protists.
The problem is that because they share a common ancestor the dividing line between animals and plants is blurred, even amongst living organisms. At this point we can only say that various protists have developed animal-like and plant-like characteristics independently on numerous occasions. IOW not all plants are closely related and not all animals are closely related.
Once again, the question can’t be answered because it is so vague.
Go down to the seashore or the edge of drying pond and look at the algae growing on the rocks or the mud. Has it made it onto land? Sure it needs to be kept moist, but is it a land plant? And if the algae aren’t land plants then what about moss? After all it needs to be kept moist too. What about ferns. And so forth.
And the same problem is faced with animals. Have whelks made it onto land? They can certainly move and feed without water, but they need to be d\submerged every few hours. How about intertidal crabs? Are they land animals? Are frogs land animals?
You really do need to define what you mean by “making it onto land” before anyone can even attempt to answer the question, and even then the answer is going to be shaky. The truth is that almost as soon as the first plant or animal evolved some species would have been exploiting intertidal or fringe zones just as they do today.
Over time the amount of time they could survive without being wetted would have increased so the line between a terrestrial flatworm and an intertidal flatworm for example or between a mudflat bryophyte and a terrestrial liverwort was totally arbitrary.
The trouble once again is that the concept is fuzzy. Higher animals can sleep because they enter a state of altered consciousness. Lower animals like worms can’t be said to sleep because as far as we can tell they don’t; have any consciousness to alter.
Plants and lower animals all show diurnal rhythms and are more or less active in daylight or darkness but that is in no way equitable to sleep.
One thing we can all agree on is that single cell can’t sleep because a single cell can not have a state of consciousness.
Single cells certainly show diurnal rhythms as expressed by algae rising and falling in the water column, but that is not sleep.
The line is once again necessarily vague because sleep is a vague term. For example most fish show distinct diurnal rhythms and most will sink to the bottom and not move when the lights go off. But is that sleep? Brainwave activity certainly alters for a ‘sleeping’ fish so I am inclined to say that fish sleep. Other people will argue that fish don’t sleep because fish don’t; have any real state of consciousness.
But if we allow fish then what about sea squirts. Do they sleep? How about jellyfish? They certainly show distinct diurnal rhythms but can a creature without a brain really be said to sleep? What about sponges? Can an animal that is essentially a collection cells really be said to sleep just because it becomes inactive at night?
Sorry these answers are so nebulous. The problem is that so many of these concepts don’t have hard and fast definitions.
All organisms require liquid water within their cells. That is universal.
However there are some organisms such as dry rot fungi and even some rodents that don’t need to take any liquid water in their diet. They can manufacture their own water chemically from their food.